# Talk:True range multilateration

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Mathematics rating:
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Field:  Geometry

## References

No citation for the proposed method for triangulation is given. Is there an evaluation that the proposed method is "good" or even "optimal" in terms of computational efficiency and/or accuracy? Is there an evaluation of the numerical stability of the proposed algorithm? Are there any comparisons with other algorithms for triangulation? — Preceding unsigned comment added by 194.138.39.52 (talk) 11:54, 16 February 2016 (UTC)

The link "Efficient Solution and Performance Analysis of 3-D Position Estimation by Trilateration" in the External Links section gives me a 404 error. daviddoria (talk) 14:34, 12 February 2013 (UTC)

As of 30 May 2014 the link points to a file hoster that shows porn when cklicking the download button. The link should probably be removed.--Jmknaup (talk) 11:28, 30 May 2014 (UTC)

http://www.globmaritime.com/technical-articles/marine-navigation/general-concepts/9622-trilateration-traverse-and-vertical-surveying.html link (reference number 3) is dead, someone should replace it with something suitable. Alenrajsp (talk) 12:31, 22 July 2016 (UTC)

## Wrong generalisation that 3/4 spheres are enough?

The article states that:

"If it is known that the point lies on the surface of a fourth sphere then knowledge of this sphere's center along with its radius is sufficient to determine the one unique location."

I'm fairly sure that this need not always be true. If you have found 2 points, that all lie on the first three spheres, then there still is an infinite number of other spheres, that also have both points on their surface. Knowing the position and radius of one of these spheres would not help to discriminate between one of the two points. To visualize: take any 4th sphere and rotate it around the axis that is defined by the two points. All spheres that are thus generated do not provide any further information. So, a 4th sphere CAN help, but it need NOT ALWAYS be enough. Or, even: there is no number N such that N spheres are guaranteed to define a single point in space via the intersection of their surfaces. One needs additional constraints as to how the spheres are positioned relative to each other. At the very least the sentence in question should be weakened to something like "is usually sufficient", if that is the case in real-world-scenarios (e.g. GPS). — Preceding unsigned comment added by 94.198.62.204 (talk) 15:21, 18 June 2013 (UTC)

When I think about it, even the statement about 3 spheres narrowing down the position to 2 points in 3D, is not correct:

"In three-dimensional geometry, when it is known that a point lies on three surfaces such as the surfaces of three spheres then the centers of the three spheres along with their radii provide sufficient information to narrow the possible locations down to no more than two."

There is actually an infinity number of different spheres in 3D that share a common "boundary-intersection-circle" (their centers lie on a straight line). I will delete the whole paragraph, because it is factually wrong and I'm not sure what it is supposed to say. --94.198.62.204 (talk) 12:41, 15 July 2013 (UTC)

The generalization holds as long as no more than 2 reference points are colinear and no more than 3 are coplanar.--Jmknaup (talk) 11:55, 30 May 2014 (UTC)

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## Dec. 2018 Edits

I added material to several sections. One intent is to show that trilateration is not just an analytic geometry problem. Real-world navigation and surveillance systems use it as well. Before my edits, the article read like a college freshman calculus homework assignment.

Second comment: GPS is not based on trilateration; it's based on multilateration (as defined by Wikipedia). I deleted that incorrect material.

Third comment: The title trilateration is a poor choice. Perhaps it reflects an academic orientation? This point is better made on the Talk:Multilateration page by the first commentor. Re-titling this article would likely require that the current multilateration article be re-titled as well, and there appears to be little interest in doing that.

As a practicing engineer for decades, I never encountered the term trilateration. (What is DME/DME aircraft navigation: bilateration? trilateration, but not literal?) I'd prefer a title like True Range Multilateration or perhaps Circular Multilateration. Then the current article entitled Multilateration would become something like Pseudo Range Multilateration or Hyperbolic Multilateration. Disambiguation might be needed as well. But a poor title is less desirable.

NavigationGuy (talk) 15:07, 30 December 2018 (UTC)

I would like to thank you for your edits to the article and remembering to include some citations as well. This area is well outside my field of expertise (I only deleted the content on the basis of wiki policy), if you feel a title change is a good idea, may I suggest (after discussion in an appropriate project if one exists), just being bold and doing it. Many thanks and kind regards EvilxFish (talk) 15:28, 13 January 2019 (UTC)
Perhaps to conclude this editing phase you might want to delete the clumsy and no longer applicable picture at the top of the page. As compensation you might also want to add some circular arcs to the other picture used to elucidate the formulas −Woodstone (talk) 05:16, 14 January 2019 (UTC)

## Jan. 2019 Edits

For the reasons given above, I changed the page title from Trilateration to True Range Multilateration. Comments welcome. NavigationGuy (talk) 15:16, 15 January 2019 (UTC)

In changing the name, I mistakenly created Category: True Range Multilation by mistake. Sorry. NavigationGuy (talk) 13:53, 18 January 2019 (UTC)